Lines Matching full:rank
817 The L-BFGS hessian approximation is a low rank approximation to the
818 inverse of the Hessian matrix. The rank of the approximation
820 approximation. Higher the rank, the better is the quality of the
830 So increasing this rank to a large number will cost time and space
833 rank. The best choice usually requires some problem specific
1892 above formula assumes that :math:`J(x^*)` has full column rank.
1894 If :math:`J(x^*)` is rank deficient, then the covariance matrix :math:`C(x^*)`
1895 is also rank deficient and is given by the Moore-Penrose pseudo inverse.
1951 Rank of the Jacobian
1954 As we noted above, if the Jacobian is rank deficient, then the inverse
1958 The rank deficiency in :math:`J` can be *structural* -- columns
1962 Structural rank deficiency occurs when the problem contains parameter
1963 blocks that are constant. This class correctly handles structural rank
1966 Numerical rank deficiency, where the rank of the matrix cannot be
1971 a. The rank deficiency arises from overparameterization. e.g., a
1976 numerical behaviour of the Solver, it will also expose the rank
1980 b. More general numerical rank deficiency in the Jacobian requires
2016 small to moderate sized problems. It can handle full-rank as
2017 well as rank deficient Jacobians.
2031 because Cholesky factorization is not a rank-revealing
2034 rank. ``SuiteSparse``/``CHOLMOD`` supplies a heuristic for
2035 checking if the matrix is rank deficient (cholmod_rcond), but it
2054 algorithm is numerically better behaved and is rank revealing,
2055 i.e., it can reliably detect when the Jacobian matrix is rank
2059 the covariance if the Jacobian is rank deficient.
2075 which is essentially a rank deficient matrix, we have
2086 :func:`Covariance::Compute` will return ``false`` if a rank
2087 deficient Jacobian is encountered. How rank deficiency is detected
2116 .. math:: \operatorname{rank}(J) < \operatorname{num\_col}(J)
2118 Here :\math:`\operatorname{rank}(J)` is the estimate of the
2119 rank of `J` returned by the ``SuiteSparseQR`` algorithm. It is
2120 a fairly reliable indication of rank deficiency.
